2004年荆州市初中数学竞赛初三

2004()(5,30)1.n(n-2004)2+(2005-n)2=1,(2005-n)(n-2004)().(A)-1(B)0(C)12(D)112.1,CGE=120.A+B+C+D+E+F=().(A)150(B)210(C)240(D)2703.xyz,zx+yxy+zyz+x.xyz().(A)zxy(B)yzx(C)xyz(D)zyx24.2,AB.AB100m,A8m/sAB60,A,7m/sB,.().(A)18s(B)20s(C)22s(D)1003s5.y=ax2+bx+c(a0),(0,1)(-1,0).S=a+b+c().(A)0S1(B)0S2(C)1S2(D)-1S16.x2-5|x|+|y|=0,y2-5|y|+|x|=0().(A)5(B)5(C)3(D)1(5,30)1.pq,5p2+3q=59.p+q=.32.3,G4ABCDBC,DEFGEFA,GD=5.FG.3.,.30,,;,,.40..4.ABC,BAC=90,BCDEDB=BC=CE,ADAE.BAD=45.,tanCAE=.5.y=x+10,y=-x+10,y=x-10,y=-x-10().(:xy,(x,y))46.4,ABC,BCP.APBCD,PB=21,PC=28,PD=.(15)k,x2+kx-k+1=0.k.(15):C(n)=12n,1n24;11n,25n48;10n,n49.n,C(n)(:).(1)n,nn?(2)5,,,60,??(15)5,ACBDOABCD,BDOC,ACPCP=OC,BPADEOF.:PFEFBF.(15)6,ABCD,AD=2,DC=4,BN=2AM=2MN,PCD,APDME,PNCMF,MEPFS.S.1.B.(2005-n)=a,(n-2004)=b,a+b=1,a2+b2=1.ab=(a+b)2-(a2+b2)2=0.2.C.AG,AGC=B+BAG,AGE=F+FAG.B+BAF+F=EGC=120.,C+D+E=BGF=120.A+B+C+D+E+F=240.3.A.xyz,x+yzy+zxz+xy.,x+y+zzx+y+zxx+y+zy.4.B.CCDABD.ts,AC=8t,BC=7t.A=60,AD=4t,CD=43t.(7t)2=(100-4t)2+(43t)2.t=20t=1003().5.B.x=0,y=1x=-1,y=0.c=1,a=b-1.S=a+b+c=2b.-b2a0,a0,2b0.b=a+1a02b2.0S2.6.A.|x|=a,|y|=b,a2-5a+b=0,b2-5b+a=0.(a-b)(a+b-6)=0.a-b=0a+b-6=0.a2-5a+b=0,a-b=0a2-5a+b=0,a+b-6=0.(a,b)=(0,0),(4,4).(a,b)=(3+3,3-3),(3-3,3+3).,(a,b)(x,y)=(0,0);4.,13.1.15.5p2+3q,pq.pq,pq2.q2,p2=535,,;p2,q=13.2.165.AG.SADG=12SABCD=12SDEFG=8,FG=165.:AEDGDC.3.961.x,y,30x+1=y(x-1).,y=30x+1x-1=30+31x-1.,x=2(),x=32.,3032+1=961.4.14.7,BCBMACCNABADAEMN.7AC=2BM,AB=2CN.tanBAD=BMAB,tanCAE=CNAC,,tanBADtanCAE=14.tanBAD=1,tanCAE=14.5.221.8,4:AOB(BO),BOC(CO),COD(8DO),DOA(AO).1+2+3+4+5+6+7+8+9+10=55,,554+1=221.6.12.ABDCPD,BDDP=ABCP.ACDBPD,DCDP=ACBP.BDDC=BPCP=34.ABDCPD,PDBD=CPAB.,PD=BDABCP=BDBCCP=3728=12.x2+kx-k+1=0ab(ab).,a+b=-k,ab=-k+1.kab-a-b=1,(a-1)(b-1)=2.a-1=1,b-1=2,a=2,b=3.k=-5.(1)C(25)=275,C(24)=288,C(23)=276,C(22)=264,C(25)C(23)C(24).C(49)=490,C(48)=528,C(47)=517,C(46)=506,C(45)=495,C(44)=484,C(49)C(45)C(46)C(47)C(48).6n(23,24,45,46,47,48),nn.(2)abS,ab.a+b=60,1a30.(i)1a11,49b59,S=12a+10b=10(a+b)+2a=600+2a,602S622;(ii)12a24,36b48,S=12a+11b=660+a,672S684;(iii)25a30,30b35,S=11a+11b=660.(36),OAH=OAM=OBM.AHB,AHB=90,,OAH+OAM+OBM=90.A=OAH+OAM=60.8.2.6.4.8.3...14a1a2akak+1a14,0akak+1.1481,,91,0.ak+1,,a1481,,ak+1a149.,10a1a2akak+1a14-a1a2ak0ak+1a14=9ak+1a14,81,81,.8.4.k,7.433,.,33k66,:(1)+(k)=(k+1),(2)+(k)=(k+2),(33)+(k)=(k+33);k,.7.4,k,;,.8.5.n=6.,n,.n=ab,abn.nns.sa2+b2+1.ab,,a2+b2+12ab+1.,sa2+b2+12ab+2=2n+2.ab,|a-b|=1,.,ab23,,n=6.8.6.a+b,a,1/;b.,1,100.300,19942000300=60.,160.8.7.7.7.(24)602-605=302,684-605=384.99,OBAF.BDOC,BO=BC.OB=OC=CP,,CP=CB.,PBC=BPC.PBD=PBC-CBD,ABP=BPC-BAC,OCBD,CBD.,BAC=DAC=CBD.,PBD=ABP.PABD.,EAF=ABF,F=F.,AEFBAF.,AF2=EFBF.FAP=FAE+CAD,FPA=ABF+BAC,CAD=BAC,FAE=ABF.,FAP=FPA,PF=AF.,PF2=EFBF.PM.DP=x,PC=4-x.AMDP,,PEEA=DPAM.,PEPA=DPDP+AM,PEPA=xx+1.SMEPSAPM=PEPA,SAPM=12AMAD=1,SMPE=xx+1.,SMPF=4-x5-x.S=x1+x+4-x5-x=2-11+x-15-x=2-6-x2+4x+5=2+6(x-2)2-92-23=43.x=2,.,S43.()